Can I allow multiple users to fill in a single form?

I need to create a form for an award nomination. Ideally, one person could go to my form and nominate someone by filling out basic information. After they complete the first section of the form, I want an email to go the the nominee. Then the second person (the nominee) would fill out a second section with their bio and head shot. 

I don't want each person to be able to edit nor see the other's section. How can I accomplish this without having to have two separate forms? I'd like all the data collection to be in one location so that I don't have to merge or update files constantly. 

You can create the forms and collect the desired data, this is what you would need to do: 

1. Create the nomination form, then there set up an email address to be sent to the second person, you can do it either with conditions or setting up an email autoresponder, here are the guides: 

https://www.jotform.com/help/26-Setting-up-an-Autoresponder-Email 

https://www.jotform.com/help/167-How-to-Send-Email-Based-on-User-s-Answer

2. The second person will be able to fill and submit the second form, now note that you will be using two separate forms so the data will be accessed separately. 

This guide will help you viewing the submissions data: https://www.jotform.com/help/269-How-to-View-Form-Submissions 

I have no problem setting up the autoresponder, but is there a way that I can do this in one form so that I will not have to access the data separately? 

Yes, you can do it, but the complexity of the form will increase as well as the resources you need to use and features you will need to implement. 

For example, you can use a single form where you will have two sections, one where the first person will enter his data and the second one where the second person will submit his information as well. 

Now, you will need to use conditions to show the fields according to the person viewing the form. This is how the process would be: 

1. Person gets the link to the form, fills the corresponding fields and submit it, an email is sent to the second person. 

2. The second person then opens the edit link and sees the corresponding fields, enter the data and submit it. 

This guide will help you doing so: https://www.jotform.com/help/389-How-to-Show-or-Hide-Fields-on-Edit-URL